MONOTONIC INDEPENDENCE ON THE WEAKLY MONOTONE FOCK SPACE AND RELATED POISSON TYPE THEOREM
- 1 June 2005
- journal article
- Published by World Scientific Pub Co Pte Ltd in Infinite Dimensional Analysis, Quantum Probability and Related Topics
- Vol. 8 (2), 259-275
- https://doi.org/10.1142/s0219025705001962
Abstract
We show how the construction of t-transformation can be applied to the construction of a sequence of monotonically independent noncommutative random variables. We introduce the weakly monotone Fock space, on which these operators act. This space can be derived in a natural way from the papers by Pusz and Woronowicz on twisted second quantization. It was observed by Bożejko that, by taking μ = 0, for the μ-CAR relations one obtains the Muraki's monotone Fock space, while for the μ-CCR relations one obtains the weakly monotone Fock space. We show that the direct proof of the central limit theorem for these operators provides an interesting recurrence for the highest binomial coefficients. Moreover, we show the Poisson type theorem for these noncommutative random variables.Keywords
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